Equidistant?

Sam and Lisa live in a city in the desert of Nevada, USA, whose altitude is equal at all points, and whose streets run perfectly north-to-south and east-to-west. They are at the intersection of Harrison Street, which is north-south, and Jefferson Street, which is east-west. They are both walking to an intersection that is a few blocks east and a few blocks south from where they are now. They both take direct routes, using only two streets each (and therefore making only one turn each), but Sam takes Harrison Street while Lisa takes Jefferson Street. Assuming that neither encounters any obstacles, and that the turns take the same distance to complete, is there any reason why Sam's path or Lisa's path could be considered longer than the other's?

Hint

Answer

Sam's route could be considered SLIGHTLY longer, though for practical purposes, the difference is negligible. Sam heads south first before heading east. Being in the Northern Hemisphere, this means that he is going closer to the Equator, where the latitude of the Earth is increased, before making the lateral component of the trip.

The effect can be made dramatically more recognizable and relevant if you imagine extremely long north-south and east-west roads. Consider a case in which you are beginning halfway between the North Pole and the Equator, and your destination is on the Equator, 1/4 of the way around the Earth laterally. The north-south component will be equal no matter which of the two routes you take. However, the east-west component must take you 1/4 of the way around the Earth in each route, which is much less halfway between the pole and the Equator, than at the Equator. Of course, no grid of roads large enough for this to be an issue exists, but it is true to a slight degree.Hide

The first thing I noticed was the category; trick.
"Harrison Street, which is north-south, and Jefferson Street, which is east-west."
Typically in the US streets run east and west and avenues run north and south.

Street name guidelines vary a lot. It doesn't seem, based on my research that I did for this teaser, that things like that are followed too strictly in most places. Good thinking, but it wasn't what I was going for

This is less a "trick" teaser, than one that depends on a knowledge of spherical geometry. And indeed, there is another answer, which does make the teaser a "trick," to wit: Lisa's path is a bit longer because "Jefferson Street" is comprised of more letters, and hence is longer, in that sense, than "Harrison Street."

I personally think it's pretty tricky. The idea is, the minds of most people, even if they have a good understanding of spherical geometry, will not think about that, because road maps are projected so that road grids look precisely square, and because the effect of the curvature is never an issue because it is extremely small.

@dsjt: You're absolutely right, that is a much more likely cause. In fact, I thought of that too, but unfortunately, it was after submitting this teaser that it crossed my mind. I have already submitted the correction, but I haven't had any corrections be approved since I joined Braingle several months ago... so I dunno if it will be done.

The difference you've pointed out is comfortably under a millimeter -- I'll bet its a few microns. It is WAY more significant that the person going east, then south is somewhat less likely to have to step around a stop sign than the person going south then east.

In any case, the extra up and down they would travel due to one sidewalk being broken and the other not would totally swamp your difference.

Agreed zag, but the point is that it takes some thought to even realize that this makes ANY difference at all, whether significant or infinitesimal. Granted it is irrelevant to the practicality of something like taking a walk... But when you consider that, for certain destinations, it could make you take an unnecessary trip 180 degrees around the equator... that's a big deal. In this teaser, it doesn't add up to anything, but the point is the fact itself, not the practical effect.